Imparfait vs Passé Composé

I was tired may be translated by J’étais fatigué or J’ai été fatigué depending on the context and what you want to say.
How to know which one we can use?

J’étais fatigué expresses a duration, an undetermined period of time.J’ai été fatigué, here you don’t mind about the duration, you want people to know how tired you were.

Undetermined timing:
I was at school J’étais à l’école (the beginning and the end are not specified, you are just describing a fact) J’ai été à l’école (you don’t insist on the period of time, but on the fact you were at school and now you are not), usually along with a word like yesterday, last week…

I loved Paris J’aimais Paris (a long time ago but it still may be true) J’ai aimé Paris (but now no!)

Some verbs according to their meaning, for example TO DECIDE, if you don’t take hours to decide something, for a past event, we will use le passé composé, j’ai décidé que…. It can depend on the context.
I studied French: if you want to insist on French, you will use the passé composé, j’ai étudié le français quand j’étais jeune.
But for a repeated action, j’étais le français tous les jours.

3. Date and Time: imparfait

It was January 10th: C’était le 10 janvier
We were on February 15: Nous étions le 15 février

It was noon: il était midi
It was 3.30 pm: il était 15 heures 30

4. Description

C’était une belle journée de printemps (you are describing a far past event)
Ça été une belle journée (but now the day is finished)
Describing things that won’t change: imparfait
Mountains for example, they were big and are still big so
C’était très grand, elles étaient très grandes
Marseille (a city), c’était beau (and it is still beautiful, you use the imparfait because you are not in Marseille right now)

Weather with the verb Faire:
Il faisait beau (the weather was nice) or Il a fait beau, both are correct, the first sentence with the imparfait expresses a duration, the second one with the passé composé emphasize the word Nice!

5. Both are possible

When I was 20 (several months), I used to live in Paris: Quand j’avais 20 ans, je vivais à Paris.
When I turned 20 (just at this age), I moved to Paris: Quand j’ai eu 20 ans, j’ai déménagé à Paris.

He wanted some apples, but there were no one left: Il voulait des pommes (Il a voulu des pommes), mais il n’y en avait plus (we imagine that this situation lasted a while so imparfait)

EXERCISE:

I had(1) a terrible weekend! On Saturday I was(2) so tired that I slept(3) all morning. When I woke(4) up I had(5) a head ache and my throat was(6) sore. My body ached(7) all over. My nose ran(8) and I coughed(9) a lot. My mother took(10) my temperature but I did not have(11) a fever.

EXERCISE:

Last night I went(1) to the Eiffel Tower in Paris. It was(2) a beautiful summer evening. It was(3) warm and sunny. Lots of people were(4) there because of the Tower. I stood(5) and watched(6) the crowd.